Chaotic oscillations of a shallow cylindrical shell with a concentrated mass under periodic excitation

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2607-2619 ◽  
Author(s):  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Mitsuru Oya ◽  
Takao Yamaguchi
Keyword(s):  
Cylindrical Shell ◽  
Periodic Excitation ◽  
Chaotic Oscillations ◽  
Concentrated Mass ◽  
Shallow Cylindrical Shell

Chaotic Oscillations of a Shallow Cylindrical Shell-Panel With a Concentrated Elastic-Support

2000 ◽  
Author(s):  
Takao Yamaguchi ◽  
Ken-ichi Nagai
Keyword(s):  
Cylindrical Shell ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Type Equation ◽  
Inertia Force ◽  
Chaotic Oscillations ◽  
Shallow Cylindrical Shell ◽  
Chaotic Response ◽  
Modes Of Vibration ◽  
Shell Panel

Abstract This paper presents numerical solutions on chaotic oscillations of a shallow cylindrical shell-panel excited by a periodic acceleration. The shell with rectangular boundary is simply supported along all edges, and the center of the shell is supported by an elastic spring. The Donnell-Mushtari-Vlasov type equation is used with the modification of an inertia force. The governing equation is reduced to a nonlinear differential equation of a multi-degree-of-freedom system by the Bubnov-Galerkin procedure. To estimate regions of the chaotic response, periodic solutions of steady state response are first calculated by the harmonic balance method. Next, time evolutions of the chaotic motion are obtained numerically by the Runge-Kutta-Gill method. The chaotic response accompanied with a dynamic snap-through is identified both by means of Lyapunov exponents and Poincaré projections. For the shell with a spring, the Lyapunov dimension is smaller than for the case without the spring. Multiple modes of vibration contributes to the generation of chaos, in paticular, the higher modes of vibration are significant.

Effects of a Concentrated Mass on Chaotic Vibrations of a Clamped Circular Plate With Initial Deformation

2011 ◽  
Author(s):  
Kenji Okada ◽  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Takao Yamaguchi
Keyword(s):  
Circular Plate ◽  
Fourier Spectrum ◽  
Principal Component ◽  
Frequency Region ◽  
Initial Deformation ◽  
Periodic Excitation ◽  
Contribution Ratio ◽  
Concentrated Mass ◽  
Chaotic Vibrations ◽  
Maximum Lyapunov Exponents

Experimental results are presented on effects of a concentrated mass on chaotic vibrations of a clamped circular plate. The plate has initial deformation due to initial deflection and initial in-plane compressive constraint at the boundary. The concentrated mass is attached on the center of the plate. Under periodic excitation, non-periodic responses with dynamic snap-through are generated on the plates. The responses are inspected by the Fourier spectrum, the Poincare´ projection, the maximum Lyapunov exponents and the principal component analysis. The non-periodic responses are found to be chaotic responses. The lowest mode of vibration shows the largest contribution ratio. When the concentrated mass is attached on the plate, the region of the response is shifted to the lower frequency. Furthermore, the width of the frequency region is decreased. The contribution ratio of the lowest mode slightly increases.

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